Similar triangles
The image provided with the question shows 3 similar triangles. The lines of length a, m, and 5 are parallel, so the lengths are proportional
The proportionality can be written as:
[tex]\frac{3}{2}=\frac{3+6}{2+4}=\frac{3+6+3}{x+4+2}[/tex]
Operating:
[tex]\frac{3}{2}=\frac{9}{6}=\frac{12}{x+6}[/tex]
The first two parts of the equalities are the same fraction (when simplified). We can use the last and the first one to find x:
[tex]\frac{3}{2}=\frac{12}{x+6}[/tex]
Cross-multiplying:
3(x + 6) = 2*12
Dividing by 3:
x + 6 = 8
Subtracting 6:
x = 2
